Related papers: Cohomological dimension theory of compact metric s…

This paper gives a short introduction into the metric theory of spaces with dilations.

We introduce a notion of equivariant coarse cohomology of the complement of a subspace in a metric space. We use this cohomology to define a notion of coarse cohomology of the configuration space of a metric space and develop tools to…

In this survey, we discuss whether the complex projective space can be characterized by its integral cohomology ring among compact complex manifolds.

Some relations between cohomological dimensions and depths of linked ideals are investigated and discussed by various examples.

In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric…

Some examples and basic properties of ultrametric spaces are briefly discussed.

In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…

A characterisation of trivial 1-cohomology for a broad class of metric spaces is presented. The condition ties cohomology and connectedness properties of open sets.

The integral cohomology ring of the complement of an arrangement of linear subspaces of a finite dimensional complex projective space is determined by combinatorial data, i.e. the intersection poset and the dimension function.

In this paper we define the coarse (co)homology of the complement of a subspace in a metric space, generalizing the coarse (co)homology of Roe. We give a model space which encodes coarse geometric structure of the complement. We also…

In this paper we give a geometric cobordism description of smooth integral cohomology. This model allows for simple descriptions of both the cup product and the integration, so that it is easy to verify the compatibilty of these structures.

This is a survey on coarse geometry with an emphasis on coarse homology theories.

The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology…

These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.

The aim of this paper is to introduce the concept of Delta-Compact spaces along with some basic properties of it. Here, we try to establish the behavior of Delta-Compact spaces under the continuous mapping. Finally, we define another…

We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…

The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…

In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces.

This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…

This is a short survey of Riemannian geometric applications of Lp-cohomology of thick spaces, p not equal to 2.